Li2FePO4F and its metal-doping for Li-ion batteries: an ab initio study

Fengmei Yanga, Weiwei Sunb, Yuhan Lia, Haiyan Yuana, Zhiyong Donga, Huanhuan Lia, Jumei Tiana, Yiying Zheng*a and Jingping Zhang*a
aNational Engineering Laboratory for Power Battery (Jilin), Faculty of Chemistry, Northeast Normal University, Changchun 130024, China. E-mail: jpzhang@nenu.edu.cn
bDepartment of Material Science and Engineering, KTH-Royal Institute of Technology, Department of Physics and Astronomy, Division of Material Theory, Uppsala University, SE-100 44 Stockholm, Sweden

Received 24th June 2014 , Accepted 29th September 2014

First published on 2nd October 2014


Abstract

The electrochemical properties of three isotopic Li2FePO4F compounds, as cathode materials under different space groups Pbcn, P[1 with combining macron] and Pnma were investigated using first principle calculations. Their structures and average open circuit voltages for step delithiation reactions were explored, and the results are in good agreement with the reported experimental data. We estimate the substitution effect of Fe by Co in Pnma-Li2FePO4F. The substitution of Fe by Co in Li2Fe1−xCoxPO4F may enhance the discharge potential of the materials, and the rate of its volume change during the redox process is between 0.6% and 2.1%. Furthermore, from the projected density of states for Li2Fe0.5Co0.5PO4F, we found strong hybridization for Fe-3d and Co-3d bands near the Fermi level, which implies that the Co-doped Li2Fe1−xCoxPO4F may possess better electronic conductivity than the pure phase.


1 Introduction

Commercialized lithium ion batteries (LIBs) have rapidly penetrated into everyday life since Sony announced the first version in 1992.1–6 Important battery performance characteristics are mainly determined by the electrochemical properties of the electrode materials, especially the cathode. The conventional positive materials for LIB such as LiCoO2, Li2MnO3 and LiFePO4 have been widely studied and optimized.7,8 For example, LiFePO4 is the most prominent compound in the transition metal polyanionic family,9,10 and its major limitations are the poor electrical conductivity and the one-dimensional Li-ion diffusion. Its relatively poor electronic conductivity can be more than offset by decreasing the size of crystallite,11 doping transition metal12 and coating conductive additives onto the surface.13 However these strategies increased the complexity and reduced the reliability of the material's manufacture, hence it is desirable to develop new polyanion-type cathode materials for lithium ion batteries. Yang et al. had reported a detailed description for this families,14 one of the most interesting poly-anion compounds is that of fluorophosphates. A2MPO4F materials (A = Na, Li; M = Fe, Mn, Co, Ni, etc.) have been proposed as promising candidates for high-energy-cathode materials, especially for A = Li.15–23

The Li2MPO4F family has attracted much attention for the following reasons: firstly, fluorophosphates compounds exhibit high specific capacity and energy density, when the exchange of more than one alkali atom per formula unit (f.u.) was considered. Secondly, it possesses facile two-dimensional pathways for Li+ transportation and the structure changes on redox are relatively small.17,20 Additionally, the high electronegativity of F serves to increase the thermal stability of Li2MPO4F compared to LiMPO4.17 Four space groups for Li2MPO4F have been widely investigated experimentally: Pnma (M = Fe, Ni, Co),18,19,21 Pbcn (M = Fe),17 P[1 with combining macron] (M = Fe),20,24 P21/n (M = Mn).16,22 Accordingly, Li2FePO4F could adopt both tetragonal and triclinic structures, which depends on synthetic procedures.17,20–22 The synthesis of Li2FePO4F remains difficult and requires either the ion exchange of the Na2FePO4F/LiNaFePO4F or a lengthy solid state reaction.17,20,21 One appealing strategy for improving the cathode properties is to develop mixed transition metal compounds,25–28 this approach has been widely applied to other material families. The influence of metal-doping on the performance of a cathode material for LIB has been investigated from both theoretical and experimental aspects.12,29–31 Nevertheless, to the best of our knowledge, the metal-doping for Li2FePO4F has not yet been reported. High-throughput density functional theory calculations had been explored and made enormous contribution to the LIB field in predicting the structural behavior and electrochemical properties. To individuate the most promising candidates for practical applications and optimize Pnma-Li2FePO4F, we investigated the electrochemical and electronic properties by metal-doping (M = Co) using ab initio methods.

Herein we systematically investigated the influence of crystal structure and relative stability on the electrochemical properties of Li2FePO4F polymorphs as cathode materials for LIB. A comparative study of three reported polymorphs crystallized of Li2FePO4F (with space groups Pbcn, P[1 with combining macron], Pnma) was also performed. Our computed structures, average open circuit voltages of Li2FePO4F are in good agreement with the experimental data. The calculated results revealed that Pnma-Li2FePO4F possesses the highest electron conductivity among investigated space groups. We explored the structure, electrochemical stability and projected density of states (PDOS) of substitution of Fe by various degree levels of Co using first principle computations as a screening tool.

2 Computational methods

All the calculations were performed by using ab inito methods implemented in the Vienna Ab Initio simulation package (VASP),32–35 which is based on the density functional theory (DFT). Generalized-gradient approximation (GGA) with the functional of Perdew, Burke and Ernzerhof (PBE) was used to describe the potential. Projector augmented wave (PAW) was employed to describe the electron wave functions.36 PAW method has been widely used for battery materials and shown excellent predictive capability.37–39 The GGA + U method was used to accurately calculate structural and electronic properties, because of the strong localization of the 3d orbital such as phosphate materials, incomplete cancellation of the self-interaction of the GGA is often reported to cause large errors.40 We used the effective U parameter for transition metals (TM), UFe = 4.5 eV,41 UMn = 4.5 eV,41 and UCo = 3.4 eV,42 respectively. A planewave cutoff energy of 400 eV was used for all computations, and appropriate k-points meshes were chosen to ensure that the total energies were converged within 2 meV per f.u. Gaussian smearing was used with a smearing parameter of 0.20 eV. The calculated energy difference between ferromagnetic (FM) and antiferromagnetic (AFM) ordering was less than 6.5 meV per f.u., implying that the magnetic structure has less effect on the energy calculations. Thus the calculations were performed in a high-spin ferromagnetic ordering. Initial magnetic moments were set to high-spin for Mn, Fe, and Co and low-spin for other elements.43

The initial atomic positions for Li2FePO4F were taken from ref. 20 (P[1 with combining macron]), ref. 17 (Pbcn), ref. 21 (Pnma), and the two Li ions were removed from the Li2FePO4F polymorphs to generate FePO4F. For the intermediate LiFePO4F, the Li-vacancy arrangements were taken from the ref. 17, 20 and 21 for Pbcn, Pnma and P[1 with combining macron], respectively. For metal-doping calculations, all structures were fully relaxed (cell parameters, cell volume, and atomic positions), and performed in an 8-f.u. Li2FePO4F supercell, in which 1–8 Fe atoms were replaced one by one by Co atom, respectively. The migration energy barriers for diffusion of Li atom are calculated by the Cl-NEB method.44

Ab initio methods have been widely used to predict the average voltages of lithium deintercalation/intercalation in many compounds.45,46 Following the well-established methods, the open circuit voltage (OCV) V vs. Li/Li+ can be calculated from the energy difference, if volume and entropy effects are neglected:7

image file: c4ra06170e-t1.tif

3 Results and discussion

3.1 Cell parameters, energy and structural characteristics of Li2FePO4F polymorphs

In this work, three Li2FePO4F polymorphs with the space groups of Pbcn, P[1 with combining macron] and Pnma are considered. Their optimized lattice parameters, volumes changes and average voltages are listed in Table 1, together with the available experimental results. For the three polymorphs of Li2FePO4F, the calculated lattice parameters are in good accordance with the experimental data, for example, the discrepancies between calculated and experimental volumes of the unit cell are lower than 2.55%. Noting that our calculated results for Pbcn-Li2FePO4F polymorph are consistent with the previous report.47
Table 1 The optimized lattice parameters, specific capacities, volume changes, and average voltages for Li2FePO4F of Pbcn, P[1 with combining macron], and Pnma space groups, compared with available results
Li2FePO4F Pbcn P[1 with combining macron] Pnma
Lattice parameter Calc Expa Refb Calc Expc Calc Expd
a From ref. 17.b From ref. 46.c From ref. 20.d From ref. 21.
a (Å) 4.99 5.05 4.95 5.34 5.37 10.61 10.78
b (Å) 13.07 13.56 13.09 7.35 7.48 6.33 6.27
c (Å) 11.37 11.05 11.17 5.35 5.33 11.13 11.03
V3) 742.06 723.60 757.62 184.64 189.14 746.8 744.5
Volume discrepancies 2.55% 2.34% 0.31%
Fe3+/Fe2+ (V) 3.27 3.50   2.43 2.75 3.50 3.40
Fe4+/Fe3+ (V) 5.20 5.09 5.02


We also compared the electrochemical properties of three compounds, the average deintercalation voltage for the first and second Li+ are show in Table 1. In P[1 with combining macron]-Li2FePO4F, Fe3+ → Fe2+ redox couple is at 2.7 V vs. Li/Li+, about 0.7 V lower than the same redox transition in Pbcn-Li2FePO4F and Pnma-Li2FePO4F. For all the polymorphs, the oxidation of Fe3+ to Fe4+ occurs at a very high voltage (∼5.1 V), which makes it necessary to use an electrolyte with a wide electrochemical window, like ionic liquids. Fig. 1 shows the calculated total energy as a function of volume obtained from the LiyFePO4F (y = 2, 1, 0). For Li2FePO4F, the total energy differences between Pbcn and Pnma-Li2FePO4F polymorphs are very small at 0 K, this phenomenon explains why synthesis of Li2FePO4F need to use ion exchange of the Na-counterparts,17,21 while for synthesized directly may easily result in a mixture of Pbcn and Pnma-Li2FePO4F. And the total energy of Pbcn and Pnma-Li2FePO4F is lower than P[1 with combining macron]-Li2FePO4F, hence P[1 with combining macron]-Li2FePO4F was less stable than Pbcn and Pnma. We stress that tavorite-type structure of P[1 with combining macron]-Li2FePO4F prepared by reduction of LiFePO4F differs greatly from ion-exchange of the Na-counterparts.20


image file: c4ra06170e-f1.tif
Fig. 1 Calculated total energy vs. volume curves for Pbcn, P[1 with combining macron] and Pnma polymorphs of LiyFePO4F (y = 2, 1, 0).

From Fig. 1, it can be observed that the unit cell volume contracts during the first and second delithiation step for both P[1 with combining macron] and Pnma-Li2FePO4F, however the unit cell volume increases for Pbcn-Li2FePO4F when it is fully delithiated to form FePO4F, this phenomena is correlated with d–p mixing.41

In Fig. 2, all Li2FePO4F polymorphs are built of FeO4F2 octahedra and PO4 tetrahedra, and each Fe atom is surrounded by two fluorine atoms and four oxygen atoms. The connectivity of the octahedral varies from the layered structure to the 3D structure.


image file: c4ra06170e-f2.tif
Fig. 2 The optimized crystal structures of three Li2FePO4F polymorphs. Pbcn: ((a) and (b)) view along the b and c axis, respectively; P[1 with combining macron]: (c) view along the c axis; Pnma: (d–f) represent the direction of [100], [011], [010], respectively. Violet octahedra, turquoise tetrahedra, and gray balls represent FeO4F2, PO4 and Li+, respectively.

Fig. 2a and b show the orthorhombic structure of Pbcn-Li2FePO4F with the layered structural features including pairs of face-sharing metal octahedra, two alkali-ions locate in the interlayer space, and two-dimensional pathways for Li+ transport.17 In the triclinic P[1 with combining macron] tavorite-type framework (Fig. 2c), the FeF2O4 octahedra forms corner-sharing 1D chain in the b axis with alternating tilted octahedral bridged by the F ions, and these chains are connected by corner-sharing the phosphate tetrahedra to create a spacious 3D structure. For the Pnma-Li2FePO4F (Fig. 2d–f), the structure consists of edge-sharing chains of FeF2O4 octahedra running along the b axis, and the channels along the [011] and [010] are capable of Li+ diffusion.

Nellie et al. also showed experimentally that the Pnma-Li2FePO4F with a 3D framework exhibits several advantages over other iron-based fluorophosphates, for instance, the volume change upon redox is one quarter of P[1 with combining macron]-Li2FePO4F and a half of Pbcn-Li2FePO4F.21

3.2 Factor-Q for three Li2FePO4F polymorphs

The search for a general quality criterion addressing the potential of three polymorphs of Li2FePO4F as cathode materials should be taken fully into account both the OCV and band gaps (BG) values. A material with a high electrochemical potential which make it an attractive candidate for cathodes used in high-energy batteries. The high OCV corresponds to a high electrochemical potential, while the low BG corresponds to high electronic conductivity of material. Mustarelli et al. raise the Quality factor, Q,25 which is proposed by combining the above-mentioned observables:
Q = OCV/BG

We calculated total density of states of Li2FePO4F/LiFePO4F (see ESI Fig. S1), the BG are determined from the calculated density of states and listed in Table 2. It is shown that both Li2FePO4F and LiFePO4F, the lowest BG values are obtained in the frame of the Pnma space group.

Table 2 The values of band gaps for Li2FePO4F and LiFePO4F with three space groups
Space group BG (Li2FePO4F)/eV BG (LiFePO4F)/eV
Pnma 3.196 1.301
Pbcn 3.465 2.578
P[1 with combining macron] 3.639 2.539


The calculated behaviors of the Q for Li2FePO4F and LiFePO4F with three space groups are presented in Fig. 3. Q values were increased from lithiated states (Purple) to delithiated (dark yellow) states of LiFePO4F. Compared with Pbcn and P[1 with combining macron] Li2FePO4F/LiFePO4F polymorphs, Pnma-Li2FePO4F/LiFePO4F may be the best cathode material with the largest Q values.


image file: c4ra06170e-f3.tif
Fig. 3 The behaviors of the Q for Li2FePO4F and LiFePO4F with three space groups.

3.3 Co-doped Pnma-Li2FePO4F

It is well known that the Co2+/Co3+ has a relatively high redox voltage. For example, fluoride phosphate Li2CoPO4F (ref. 19, 48 and 49) possesses the highest redox potential among available cathodes currently (5.1 V vs. Li/Li+). It can be expected that the substitution of Co for Fe at Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1) may increase the discharge potential (i.e. energy density) of the materials. Moreover, Pnma-Li2CoPO4F is isostructural with Pnma-Li2FePO4F, hence Co-doped Pnma-Li2FePO4F, i.e. Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1), may not occur a phase transformation like Na2Fe1−xMnxPO4F.50 Previous report revealed that the Li2MnPO4F belongs to the P21/n space group,16 for comparison, we investigate the stability of the Co/Mn-doped Pnma-Li2FePO4F as well (see detail in the ESI). The calculated results suggest that Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1) is stable enough as a new cathode material, but Li2Fe1−xMnxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1) might easily decomposed into LiMnPO4, LiFePO4 and LiF (as illustrated in Fig. S2 in ESI). This can be traced back to the isostructural of Li2CoPO4F with Pnma-Li2FePO4F, while Li2MnPO4F is different. Hereafter, we estimate the structure, electrochemical properties and PDOS of Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1) in the following calculations.
3.3.1 The lattice parameters of Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8). The lattice parameters and unit cell volume for Li2Fe1−xCoxPO4F (0 < x < 1) are summarized in Fig. 4. The a and b lattice parameters almost remain the same upon the substitution of Fe by Co, while c values are decreased. As a result, the unit cell volume of Li2Fe1−xCoxPO4F should decrease with the substitution of Co for Fe, because of the ionic radius FeII > CoII (CoII: 0.745 Å, FeII: 0.780 Å for high-spin state within six-fold coordination).51 To evaluate the affect of decrease volume to the Li conductivity in the materials, we also calculated the activation barriers of Li2Fe1−xCoxPO4F (x = 0, 0.25, 0.75) in the ESI (Fig. S5). It is found that the higher doping concentration leads to higher migration barriers for diffusion of Li.
image file: c4ra06170e-f4.tif
Fig. 4 The unit cell parameters and volumes for different compounds of Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8).
3.3.2 Most probable doping model. There are two distinct positions for Fe, namely Fe(1) (4a sites) and Fe(2) (4b sites) in Pnma-Li2FePO4F structure though they have same coordination environments (ESI, Fig. S3). From Table 3, it is clear that the Fe–X distances and the O–Fe–O/F angles are different for Fe(1)O4F2 and Fe(2)O4F2 octahedra. The distance of Fe(1)–O (2.08 Å) and Fe(2)–O (2.05 Å) are similar, while the average bond length of Fe(2)–F is ∼0.1 Å longer than that of Fe(1)–F. The increasing of Fe–F distance may cause the decrement of static electricity, and Co may be inclined to substitute for Fe(2) (4b sites) atom. Pnma-Li2FePO4F has some distortion in the Fe(1)O4F2 and Fe(2)O4F2 octahedra, which may reduce the structural stability. For instant, the higher distortion of angles of O–Fe(1)–O/F than those of O–Fe(2)–O/F may results in the higher instability of Fe(1)O4F2 octahedra structure.
Table 3 Optimized Fe–O/F average lengths and angles of O–Fe–O/F
Bonds Average Length (Å) Angle Value (°)
Fe(1)–O 2.08 O–Fe(1)–O 84.99
Fe(2)–O 2.05 O–Fe(2)–O 85.61
Fe(1)–F 2.13 O–Fe(1)–F 101.42
Fe(2)–F 2.22 O–Fe(2)–F 97.94


We calculated the energies of 23 configurations for Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1), in the Pnma host, using the supercells up to 8-f.u. (Li16Fe8P8O32F8). In Fig. 5, we displayed the total energies (in black) and unit cell volume (in red) for most stable substituted Li2Fe1−xCoxPO4F (0 < x < 1), where the labels (1) and (2) refer to positions of Fe.


image file: c4ra06170e-f5.tif
Fig. 5 The calculated energies and unit cell volume for Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8).

From Fig. 5, it is evident that the substitution of Co for Fe(2) at Li2Fe1−xCoxPO4F possesses lower energy values than Fe(1). Consequently, Fe(2) may be more favorable in the Co substitution than Fe(1). When x = 0.375, the energy for 222 site is only 0.85 meV per f.u. higher than that of 221 site, nevertheless, such a small value is at the range of error limitation. For the different concentrations of 12.5%, 25%, 37.5%, the trend is that the most stable multicomponent fluorophosphates compounds (with lower total energy) have the largest volume. However, no direct correlation between the volume and the total energy were observed at other concentrations. We also calculated the energies of vacancies of Fe(1) and Fe(2), and the results show that Fe(2) vacancy has lower total energy, consequently, Co may substitute the Fe atom at the Fe(2) site preferentially.

3.3.3 OCV. It is instructive to investigate the electrochemical parameter OCV, which usually contains enough information to decide whether a material is of interest as a cathode candidate for Li-ion batteries.41 Fig. 6 shows the two voltages corresponding to the extraction of two Li ions in two consecutive electron redox processes. These results also confirmed our former prediction that the substitution of Co for Fe at Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8) can increase the discharge potential of the material. Interestingly, the first voltage step (y from 2 to 1) increases 0.1 V, when the concentration of Co increases by 12.5%, while the fully delithiated voltage step (y from 1 to 0) increases by about 0.02 V with the substitution of Co for Fe. The volume changes of Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8) upon redox are in the range of 0.6–2.1% (see ESI, Fig. S4), which is smaller than that of LiFePO4 (6.7%), indicating that Li2Fe1−xCoxPO4F is stable enough to be new cathode materials.
image file: c4ra06170e-f6.tif
Fig. 6 The calculated total energy for LiyFe1−xCoxPO4F in the lithiated (y = 2), semi-delithiated phase (y = 1) and full-delithiated phase (y = 0) together with the calculated cell voltages.
3.3.4 Electronic structure of Li2Fe1−xCoxPO4F. To evaluate the electron properties we calculated the electronic structure of Li2Fe1−xCoxPO4F. Fig. 7 shows the PDOS onto the d-orbital of the TM of the Li2Fe1−xCoxPO4F (x = 0.25, 0.375, 0.5, 0.75). Only electron states near the Fermi level play the key role in the electron transport processes, thus we mainly focus on the PDOS around the Fermi energy. Careful inspection of Fig. 7 demonstrates that there are two parts in the DOS patterns around the Fermi level those are un-completely filled 3d orbitals of transition metal located below the Fermi level, and empty 3d orbitals located above the Fermi level.25 For Li2Fe0.75Co0.25PO4F that is x = 0.25 both valence and conduction states are mainly contributed from Fe 3d orbitals. When x = 0.375 the conduction bands localized about 3.0 eV are mainly due to Co-3d states and this configuration leads to a lower BG, while for x = 0.75, the energy region just above Fermi level dominated by unoccupied Co 3d orbitals. It is interesting to note that at the concentration of 50%, i.e. Li2Fe0.5Co0.5PO4F, the occupied Co-3d states are strongly hybridized with the Fe-3d states near the Fermi level. The Li2Fe1−xCoxPO4F can be considered as semiconductor at the Co concentration of x = 0.25, 0.375, and 0.75; while this material shows metallic at x = 0.5. To investigate the difference electronic properties of Li2Fe1−xCoxPO4F (x = 0.25, 0.5, 0.75), we plotted the electron localization function (ELF) in the ESI (see Fig. S6). Thereby with the increasing of Co doping content, the contribution of 3d orbital of cobalt to the TDOS around the Fermi level is increases correspondingly. Thus, the Co-doped Li2FePO4F may have better electronic conductivity than the pure phase.
image file: c4ra06170e-f7.tif
Fig. 7 The calculated PDOS of Li2Fe1−xCoxPO4F (x = 0.25, 0.375, 0.5, 0.75), PDOS for different atoms are denoted by different colors to indicate their contribution.

4 Conclusion

We have investigated the Pbcn, P[1 with combining macron] and Pnma space groups of Li2FePO4F by using first-principle DFT computations. The calculated average intercalation voltages, as well as the lattice parameters, agree well with available experimental results. In particular, Pnma-Li2FePO4F is interesting as far as the electron conductivity is concerned. For transition metal doped Pnma-Li2FePO4F, Li2Fe1−xCoxPO4F may be stable enough to be used as new cathode materials. Furthermore, the substitution of Co for Fe i.e. Li2Fe1−xCoxPO4F (0 < x < 1) favors to increase the discharge potential of the pure materials, although the migration barriers for diffusion of Li are increased to some extent as well. The small volume change (0.6–2.1%) on the removal of one or two Li+ per f.u., suggests that Li2Fe1−xCoxPO4F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8) is stable enough to be utilized in the cathode materials. The PDOS of Li2Fe0.5Co0.5PO4F shows both Co-3d and Fe-3d states contributing to the electronic states around the Fermi level, indicating it may possess better electronic conductivity than the Pnma-Li2FePO4F.

Acknowledgements

Financial support by the NSFC (21173037 and 21274017) is gratefully acknowledged.

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Footnote

Electronic supplementary information (ESI) available: (S1) The total DOS of Li2FePO4F and LiFePO4F. (S2) The stability of Li2Fe1−xMxPO4F (M = Co, Mn). (S3) Positions of Fe in Pnma-Li2FePO4F. (S4) Volume changes of Li2Fe1−xCoxPO4F upon delithiation. (S5) Migration barriers for diffusion of Li atom in Li2Fe1−xCoxPO4F. (S6) The electron localization function (ELF) of Li2Fe1−xCoxPO4F (x = 0.25, 0.5, 0.75). See DOI: 10.1039/c4ra06170e

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